The DOI matches its Crossref record; 30 of the 30 references it cites were found in a registry or an index.
Sparse permutation invariant covariance estimation
Open accessAbstract
The paper proposes a method for constructing a sparse estimator for the inverse covariance (concentration) matrix in high-dimensional settings. The estimator uses a penalized normal likelihood approach and forces sparsity by using a lasso-type penalty. We establish a rate of convergence in the Frobenius norm as both data dimension p and sample size n are allowed to grow, and show that the rate depends explicitly on how sparse the true concentration matrix is. We also show that a correlation-based version of the method exhibits better rates in the operator norm. We also derive a fast iterative algorithm for computing the estimator, which relies on the popular Cholesky decomposition of the inverse but produces a permutation-invariant estimator. The method is compared to other estimators on simulated data and on a real data example of tumor tissue classification using gene expression data.
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Citations
Cites
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Metadata
- Authors
- Rothman, A. J., Bickel, P. J., Levina, E., & Zhu, J.
- Venue
- Electronic Journal of Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 2008-01-01
- Volume
- 2
- Issue
- none
- Pages
- 494-515
- ISSN
- 1935-7524 (ISSN-L)
- OpenAlex
- W1974105260
- Cited by
- 560
- References
- 30
- FWCI
- 16.14
- Type
- journal article
- Language
- en
- Open access
- gold
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
